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IV. Thermodynamics Applied to Potassium Exchange in Soils and Clay Minerals
investigated K exchange using thermodynamic techniques (Jensen, 1972,
1973a,b, 1975; Jensen and Babcock, 1973) but based on equations developed by
Argersinger et al. (1950) (see Section &A).
The following parameters are derived from a thermodynamic analysis of cation exchange, presented with their physical interpretation.
1. The exchange isotherm (Fig. 1) relates the equivalent fraction of the
adsorbed cation with its equivalent fraction in solution. It can be used to indicate
selectivity in an exchange process under certain conditions (see later) or to
calculate selectivity coefficients. Exchange isotherms were classified by Sposito
(1981b) into four common types, depending on their behavior at low values of
the ordinate and abscissa (Fig. 5): (a) S type, indicative of an exchangeable ion
whose relative affinity for the exchanger is not large; (b)L type, indicative of an
ion with a high relative affinity for an exchanger; (c) H type, an extreme case of
an L type; and (d)C type, a linear isotherm indicative of nonpreference. Isotherms for K+-Ca2+ exchange have been found to be S type (Hutcheon, 1966),
L type (Jensen, 1973a), and H type (Deist and Talibudeen, 1967a), depending on
temperature, concentration, and the exchanger. Isotherms can vary greatly with
ionic strength (see Sposito, 1981b), hence the need for caution when interpreting
them. However, an isotherm at one concentration can be used to calculate isotherms at any other concentration for the same cation pair, temperature, and
exchanger (Section 11,C).
2. The (corrected) selectivity coefficient (K,) expresses the selectivity of an
exchanger for a pair of cations at a certain cation ratio. It is less ambiguous than
the exchange isotherm because it is virtually independent of ionic strength (Barrer and Klinowski, 1974; Sposito, 1981b). A plot of K,, or as is more commonly
used, In K,, against fractional saturation gives a quantitative indication of selectivity changes during an exchange reaction.
FIG.5. The four classes of exchange isotherm. Sposito (1981b).
THERMODYNAMICS AND POTASSIUM EXCHANGE
3. The Gibbs free energy of exchange (AGO) expresses the overall selectivity
of an exchanger at constant temperature and pressure, and independently of ionic
strength. It has been called the driving force of a reaction. For A 4 B exchange,
a negative AGO implies that B is the preferred or selected cation, and vice versa.
4. The enthalpy of exchange (A@) indicates the relative binding strength of
the two cations and forms one part of the driving force (AGO) of a chemical
reaction according to
AGO = AHO - T A P
5 . The entropy of exchange (AS”)expresses the difference in degree of order
of all components of the exchange between the two homoionic forms of the
exchanger. It is the second part of the driving force of a reaction according to Eq.
(29). Entropies have been used to assess the relative importance of solid and
solution phase changes in exchange reactions (e.g., Hutcheon, 1966; Deist and
6. Adsorbed-ion activity coefficients u> reflect the fugacity of an adsorbed
ion. Fugacity is the degree of freedom an ion has to leave the adsorbed state,
relative to a standard state of maximum freedom of unity. Plots off versus
fractional saturation therefore show how this “freedom” alters during the exchange, thus indicating exchange heterogeneity.
7. Excess thermodynamic functions also indicate’departurefrom ideality and
thus heterogeneity but allow for the behavior of both cations (Talibudeen, 1971).
8. Integral and differential thermodynamic functions show how free energy,
enthalpy, and entropy vary during an exchange reaction. Differential free energies are calculated directly fi’om selectivity coefficients (Section II1,B) and so
give no more information than do the latter. However, directly measured differential enthalpies give a clear picture of exchange heterogeneity and provide
another means of investigating surface chemistry. Differential entropies, although complex, can interpreted in terms of the structural order of all the components of the exchange system.
In presenting the physical interpretation of the latter three sets of parameters,
“exchange heterogeneity” has been mentioned (see also Sections II,E,F and
111,B). Heterogeneity of exchange is caused by one or more of the following: a
heterogeneous distribution of ions on the exchanger; a heterogeneous distribution
of exchange sites in terms of their position and energy; differences in the properties of the two cations (e.g., size, polarizability, and hydration); in soils, a
heterogeneous clay mineralogy and a complex mixture of organic and inorganic
The application of thermodynamic reasoning to cation exchange in soils and
clays, and of the Gaines and Thomas method in particular, is not without problems. The method assumes a constant exchange capacity and a negligible adsorp-
KEITH W.T. GOULDING
tion of anions from solution. The latter is usually true for cation exchange in soils
and clays in dilute solutions. However, the CEC has been found to change during
an exchange experiment, particularly for K+-Ca2+ exchange where some K+
may be fixed. Faucher and Thomas (1954) estimated that a change in CEC from
123 to 135 p q / g during Cs+-K+ exchange affected the isotherm by about 4%
and was thus negligible. Hutcheon (1966) found a similar change in CEC during
K+-Ca2+ exchange and therefore ignored it. However, Deist and Talibudeen
(1967b) showed more satisfactorily that the decrease in CEC during Ca2+ --f
K + exchange in their experiments on soils resulted from Ca2+ ions trapped
inside the exchanger and not from an irreversible fixation of K + . They therefore
suggested that if exchange sites were homogeneously distributed and some sites
were physically restricted, the thermodynamic treatment was not invalidated.
This view was supported experimentally when Goulding and Talibudeen (1980)
obtained identical plots of In K, versus K + saturation (and thus identical AGO
values) and identical AHO values for Ca2 --f K and K + Ca2 exchange on
a montmorillonite, a kaolinite, and a vermiculite clay.
Deist and Talibudeen (1967b) also discussed the problem of extrapolating
exchange isotherms, and thus of calculating K, values, at very small saturations
of the preferred ion where selectivity is high. They thought that a linear extrapolation was reasonable but could not estimate the errors involved. Sposito and
Mattigod (1979) and Sposito (1981a,b) questioned the thermodynamic meaning,
and thus the application, of adsorbed-ion activity coefficients and selectivity
coefficients as calculated by the Gaines and Thomas method. This problem was
discussed by Goulding (1983); the argument is summarized in Section II,E.
Studies of the thermodynamics of potassium exchange have concentrated on
either the comparison of the exchange properties of K + with those of other
cations or the comparison of a series of soils or clays using potassium exchange
with another cation as the reference point. The research will therefore be reviewed under these main headings, with special sections discussing potassium
selectivity and furation, and potassium potentials.
The reviews by van Blade1 (1967, 1972) cover the early research in this area.
The main aspects are the following:
1. Comparison of cation selectivities
2. Estimation of the relative effects of ionic polarizability and hydration
3. Comparison of the relative contributions of enthalpy and entropy to free
4. Use of exchange parameters for A-B exchange and A-C exchange to
predict those for B-C exchange (Hess’s triangle rule)
THERMODYNAMICS AND POTASSIUM EXCHANGE
5 . Use of selectivity coefficients, adsorbed-ion activity coefficients, and ex-
cess thermodynamic functions to elucidate the behavior of the exchange
complex in detail at various compositions of the exchange sites.
The topic is best covered under the headings homovalent and heterovalent
1. ffomovalent Exchange
Martin and Laudelout (1963) comprehensively examined the exchange of
NH, with Na , K , Li ,Rb , and Cs on Camp Berteau montmorillonite.
Selectivity, as expressed by In KL and AGO, was a function of ion polarizability
(z /r, where z is the ion charge and r is the radius of the anhydrous cation).
The order of selectivity for the monovalent alkali metal cations was that of the
Hofmeister or lyotropic series Cs > Rb > NH, = K > H,O > Na >
Li+ [the ionic radii of these anhydrous cations, in nanometers, are as follows:
Cs+, 0.167; R b + , 0.147; NH4+, 0.143; K + , 0.133; Na + , 0.097; and L i+ ,
0.068 (Weast, 1971); those of the hydrated cations are Cs+, 0.228; Rb+ ,0.228;
K + , 0.232; Na+ , 0.276; and Li+ , 0.340 (Cotton and Wilkinson, 1972)l. The
K + + M2+ exchange on a montmorillonite gave similar results for divalent
cations (van Bladel, 1967): Ba2+ > Sr2+ > Ca2+ > Mg2+ [where the
anhydrous ionic radii are Ba*+, 0.134; Sr2+, 0.112; Ca2+, 0.099; and Mg2+,
0.066 (Weast, 1971)l. It is interesting to note that the reverse order was found for
Na+ -+ M2+ exchange on vermiculite by Wild and Keay (1964) because of the
different characteristics of the Na+ ion and vermiculite.
Deist and Talibudeen (1967a) obtained AGO and adsorbed-ion activity coefficient values for K -Na+ and K -Rb exchange on soils, which again gave
the order of preference Rb+ > K+ > Na+ . The widely contrasting soils
differed little in their selectivities. The mean AGO value for Na+ 3 K + exchange was -4.08 & 0.29 kJ/eq; for Rb+ -+ K + exchange it was -2.11 2
0.36 kJ/eq. By contrast the same soils exhibited AGO values for Ca2+ -+ K+
exchange ranging from -4.40 to - 14.30 kJ/eq. Adsorbed-ion activity coefficients showed that for K + -+ Na+ exchange (two ions of the same valency but
different in size and thus in selectivity), fugacity for each ion increased smoothly
with increasing saturation (Fig. 6). For K+-Rb+ exchange [two monovalent
ions of very similar size and selectivity and thus with almost ideal behavior
(Section &A)], fugacity changed very little from the standard state value of 1.
Therefore, for homovalent exchange potassium selectivity is a function of its
polarizability (i.e., its size only).
Gast and co-workers (Gast, 1968, 1969, 1972; Gast et al., 1969) found the
same selectivity series again for alkali metal cation exchange on Wyoming
bentonite and Chambers montmorillonite; it was not changed by pH. They found
FIG. 6. Adsorbed ion activity coefficientsfK (0)and fNa (m) as a function of hctional K +
saturation x for K+-Na+ exchange on soils. Deist and Talibudeen (1967a).
that selectivity was determined primarily by the enthalpy term, counterbalanced
by a smaller entropy term, but that entropy changes became more important as
the surface charge density of the clay increased. They concluded from these
observations that selectivity was governed chiefly by electrostaticforces between
hydrated cations and the surface, and assumed that all changes in entropy resulted from changes in ion hydration. Work on Na -Cs exchange on clays
(Maes and Cremers, 1978) has supported the former conclusion, but not the
2 . Heterovalent Exchange
More research effort has been expended on heterovalent exchange than on
homovaknt exchange because the former is generally of greater agricultural and
industrial importance. Results can be separated into mono-divalent, monotrivalent, and di-trivalent exchange.
a. Mono-Divalent Exchange. From the early work, particularly of Hutcheon
(1966), Deist and Talibudeen (1967a,b), and Laudelout et al. (1968a,b), and
from the more recent work of Goulding and Talibudeen (1980, 1984a,b) and
Talibudeen and Goulding (1983a,b), several conclusions can be drawn.
1. It is unwise to use the exchange isotherm to assign selectivity because it
varies greatly with ionic strength and may show hysteresis. Deist and Talibudeen
(1967b) suggested that the ionic strength effect resulted mainly from entropic
2. Overall selectivity is best expressed by K or AGO, and changes in selectivity during the exchange process are best expressed by a graph of In K,, or the
differential free energy, versus K+ saturation. In heterovalent exchange, AGO
THERMODYNAMICS AND POTASSIUM EXCHANGE
depends on ion size and valency, that is, the coulombic or charge factor. Thus
AGO for Ca2 ---* Na2 exchange in soils is usually positive (Poonia and Talibudeen, 1977) and for Ca2+ ---* K + exchange it is usually, although not always,
negative (Deist and Talibudeen, 1967b). Thus Goulding and Talibudeen
(1984a,b) found AGO for Ca2 + K exchange on 14 soils to vary greatly (from
+2.2 to - 10.0 kJ/eq) depending on mineralogy, pH, fertilizer, cropping history, and organic matter content.
3. The relative binding strength between two cations and the surface is
expressed by the enthalpy of exchange (Hutcheon, 1966). Laudelout et af.
(1968a) for M2+ + NH4+, and Hutcheon (1966), Deist and Talibudeen
(1967b), and Goulding and Talibudeen (1979, 1980, 1984a,b) for Ca2+ + K +
exchange, found that AtP was negative, implying stronger binding for K + ,
NH, , and, by implication, other selectively adsorbed cations such as Rb and
Cs+. In addition, Goulding and Talibudeen (1984a,b) found that although this
greater binding strength for K + in soils may be slightly decreased by K +
fertilizer treatment, it never reverses to make Ca2+ the more strongly bound,
even after 140 years of heavy FWM or inorganic K + fertilizer applications.
The reaction M2+ --* K + becomes increasingly exothermic (i.e., the binding
strength for K + increases) as the polarizability of M2+ decreases (van Bladel,
1967). This is because the less easy a cation is to polarize, the less easily it
displaces K , and the stronger, relatively, is the K -surface bond.
4. The entropy of exchange expresses the rearrangement of cations, surfaces, and solvent molecules during the exchange process. Hutcheon (1966) and
Deist and Talibudeen (1967b) found AF for Ca2+ + K + exchange on soils to
be negative. They attempted a qualitative discussion of entropy changes in the
solid and solution phases, and concluded that those in the solution phase must
dominate, as they are large and negative for the K (solution) to Ca2 (solution)
exchange. However, Goulding and Talibudeen (1980) found that Ca2+ + K +
exchange on clay minerals was accompanied by a negative AF value for the
expanded 2:l minerals vermiculite, illite, and montmorillonite, but by a positive
AF value for the collapsed 2:l mineral muscovite mica. They therefore suggested that rearrangements within the solid phase contribute most to entropy
changes. (For a full discussion, see Section IV,C.)
5 . Adsorbed-ion activity coefficients and excess functions for Ca2 + K
exchange showed a marked difference in the behavior of Ca2+ and K + ions.
Although the fugacity of Ca2+ decreased smoothly as K + saturation increased,
that of K + varied greatly, the graph of fK versus K saturation showing maxima, minima, and inflections (Talibudeen, 1972) (see Fig. 2A). This was taken
as reflecting the different distributions of Ca2+ and K + ions in the Gouy and
Stem layers (Deist and Talibudeen, 1967a). The interpretation with respect to the
surface is given in Section IV,D,l.
It is interesting to note that the behavior of the selectively adsorbed K ion, as
shown byf,, was influenced by both enthalpic and entropic forces, whereas that
of the nonselectively adsorbed Caz+ ion depended only on entropic forces
(Goulding and Talibudeen, 1980). This suggests the primacy of strength of
binding in determining K+ selectivity and fixation (but see Section IV,E,l
where the relative importances of enthalpy and entropy are discussed in full).
b. Mono-Trivalent Exchange. The only work on the thermodynamics of
mono-trivalent exchange has been on K -AP exchange by Coulter (1969),
Sin& and Talibudeen (1971), and Sivasubramaniam and Talibudeen (1972),
which is summarized by Talibudeen (1972, 1981). Aluminium dominates the
exchange complex in strongly leached acidic tropical soils. However, its ionexchange behavior is complicated by the existence of polymeric A l - O H forms
at pH values above 4. For example, the precipitation of A l - O H polymers as
“islands” in the interlayer space of 2:1 minerals prevents their collapse on K
adsorption and thus prevents K+ fixation (Rich, 1972). Experiments at low pH
values have clarified the K+-A13+ exchange process.
Although exchange isotherms suggested A13 preference in all soils and clays
(vermiculite, illite, and montmorillonite) examined, In K, and AGO values indicated K + preference in seven out of nine soils and all three clays (Talibudeen,
1972). It is important to note that if what Coulter (1969) called “difficultly
exchangeable K ’ is ignored when calculating K, values, results sometimes
suggest A13+ preference. However, this K + should be included in the calculations because it indicates strong K+ preference over the first 20-30% of
exchange because of specific (ion-size) effects. Illite,
montmorillonite, and soils dominated by these minerals exhibited greatest preference for K + and less for vermiculite and chlorite. The presence of organic matter
also decreased the preference of a soil for K over AP ,because organic matter
chelates polyvalent, but not monovalent, cations (Talibudeen, 1981).
The more strongly leached the soils (and therefore the less 2:l clay minerals
present), the lower was the preference for K + . Indeed, when devoid of such
minerals, soils preferred A13 , presumably because in other minerals there is no
effect of ion size and valency alone controls selectivity. As in K -Ca2 exchange, fK versus K + saturation curves showed maxima and inflections, andf,,
versus K + saturation curves changed smoothly (see Fig. 2B). This again shows
the contrasting behavior of selectively adsorbed (K+) and nonselectively adsorbed (A13+) cations.
c. Di-Trivalent Exchange. Only Ca2 -A13 exchange has been investigated (Coulter and Talibudeen, 1968). For vermiculite, illite, montmorillonite, and
two acidic (pH 4.8) soils, exchange isotherms and In K, values showed strong
A13+ preference which decreased with surface charge density for the clays,
illustrating the importance of coulombic (charge or valency) effects in the exchange of such strongly hydrated ions.
THERMODYNAMICS AND POTASSIUM EXCHANGE
Potassium exchange with other cations has been used to examine and compare
clay minerals (aluminosilicates), but only recently have thermodynamic methods
been used for a systematic comparison of a suite of minerals. Homovalent
exchange shows little difference between exchangers for any one cation pair, as
was shown in Section IV,B, 1. Heterovalent exchange is therefore used, the main
reference cation pair involved being K+-Ca2+ with, to a lesser extent,
K+-A13+. Potassium selectivity and fixation in clays have also been of great
interest, but these are considered separately in Section IV,E.
Hutcheon (1966), examining K + -Ca2+ exchange on Chambers montmorillonite, related entropy changes to changes in lattice spacing and cation and
surface hydration, and enthalpy changes to cation binding strength. He also
related variation in the adsorbed-ion activity coefficients with changing K
saturation to changes in lattice spacing. His aim was to segregate solid and
solution effects, and, the behavior of ions in solution being fairly well defined, to
learn more about those which occurred in the solid phase. He concluded that the
overall exchange reaction was governed by a balance of interlayer cation hydration forces and attraction forces between the cations and the surface. A similar
conclusion was reached by Gast (1969, 1972) and Gast et af. (1969).
Although Hutcheon’s (1966) work was extremely thorough, it could be argued
that he arrived at no new conclusions regarding clay properties, particularly for
montmorillonite which had been extensively examined by other methods (e.g.,
Norrish, 1954). However, he was the first to apply thermodynamic methods
specifically to K + exchange and to attempt a physical interpretation of the
resulting data. He thus opened the way for a comparison of the more important
clay minerals, which is of much greater interest than studies of a single clay or
Goulding and Talibudeen (1980) examined five aluminosilicate minerals
chosen as representatives of groups of aluminosilicates commonly occurring in
soils. They were a muscovite mica from Norway, Fithian illite, Montana vermiculite and Upton (Wyoming) montmorillonite from the United States, and a
kaolinite from England. Free energies of exchange indicated that all of the
minerals selectively adsorbed K + , selectivity decreasing in the order mica >
vermiculite = illite > kaolinite > montmorillonite. Excepting kaolinite, this is
approximately the same order of selectivity as that suggested by Talibudeen
(1971) based on K -Ca2 exchange in soils and mineralogical data for those
soils and identical to that found by Assa (1976a,b), who examined K+-Ca2+
exchange on a similar suite of minerals using Gapon’s constant. Because kaolinite is usually considered to have a very low preference for K if not actually
preferring Ca2 ,the kaolinite examined by Goulding and Talibudeen (1980) had
an anomalously high K + preference. A reason for this became apparent when
KEITH W. T. GOULDING
FIG. 7. Differential enthalpy of exchange, [d(AHx)/)ldx)],as a function of fractional K+ saturation, x, for a Montana vermiculite and an English kaolinite. After Gouldmg and Talibudeen (1980).
the enthalpy values, and particularly the differential enthalpy curves, were examined. From the AH” values, the order of decreasing binding strength for K + was
mica > illite = kaolinite > vermiculite > montmorillonite. Again, the kaolinite
occupies an anomalously high position. Its differential enthalpy values were the
same, within experimental error, as those of the Montana vermiculite (Fig. 7).
Only the disribution of enthalpy values was different; there were about 160
p q / g of strong K binding sites in the vermiculite and only 19 peq/g of these
sites in the kaolinite. This suggests, therefore, that the presence of about 2% by
weight of a vermiculitic impurity [i.e., weathered micaceous interleaves of the
type shown by Lee et al. (1975) using scanning electron microscopy] is responsible for the exchange characteristics of the kaolinite (see also Lim et al., 1980).
The same effect can be seen in some data of Bansal (1982) on K+-Ni2+
exchange in a kaolinite from Bath, South Carolina (United States). The Lw” and
AGO values indicated a stronger binding and selectivity for Ni2+. However, plots
of K,,fK, AGE, and M Eversus Ni2+ saturation all suggested the existence of a
few sites (about 20 w q / g of a total CEC of 107 peq/g) which had high selectivity
for K . The differential enthalpy curves of Goulding and Talibudeen (1980) also
suggested the presence of a small amount of mica in the montmorillonite, modifying its exchange properties.
Subsequent research on kaolinites and montmorillonitesfrom different sources
(Talibudeen and Goulding, 1983a,b) has shown that virtually no so-called
montmorillonite is completely free of micaceous impurities (the < 0.2 pm
fraction of an Upton montmorillonite was the only “pure” sample found), and
that all of the cation-exchange properties of kaolinites can be explained by 2:l
mineral impurities. Such detailed quantitative mineralogical analyses, which
have hitherto been impossible using X-ray diffraction techniques, thus open up
new possibilities in analysis.
THERMODYNAMICS AND POTASSIUM EXCHANGE
Integral and differential entropy values of the five minerals studied by Goulding and Talibudeen (1980) supported to some extent Hutcheon’s (1966) view of
the importance of lattice expansion and contraction, but not the dominance of
solution forces over solid effects. X-ray diffraction evidence by Plancon et al.
(1979) had suggested that montmorillonite surfaces rearrange and reorder before
collapsing when the mineral is subjected to wetting and drylng cycles following
K -Ca2 exchange. Based on this and their own data, Goulding and Talibudeen (1980) suggested three physical mechanisms that contribute to entropy
changes during Ca2 +-K exchange in clays: (1) in the solid phase, replacing
Ca2+ by K+ realigns the aluminosilicate layers in the 001 direction such that the
hexagonal holes in adjacent sheets can accommodate K + ions [as suggested long
ago by Jackson (1963)], resulting in a negative entropy change; (2) in the solid
phase again, replacing Ca2+ by K + increases the randomness of distribution of
exchangeable cations, resulting in a positive entropy change; (3) in the solution
phase, replacing K + by Ca2+ increases the structural order of water molecules,
decreasing the entropy of the system. The fact that all the expanded 2: 1 minerals
examined exhibited negative entropy changes during Ca2+ + K + exchange,
whereas muscovite mica, a collapsed 2: 1 mineral, exhibited a positive entropy
change, suggested that the solid-phase effects (1) and (2) dominate.
Adsorbed-ion activity coefficients gave little new evidence on mineral characteristics, but agreed quantitatively with differential enthalpy values as to the
disposition of site groups (see Section IV,D,I).
1. Temperate Soils
Deist and Talibudeen (1967a,b) first used a thermodynamic treatment of cation exchange to compare soils, examining K+-Na+, K+-Rb+, and
K -Ca2 exchange on 10 important British arable soils. The clay content of the
soils ranged from 13 to 4396, the pH ranged from 5.4 to 7.1, and the CEC
(measured by M NH,Ac leaching at pH 7) ranged from 124 to 307 Feq/g. Little
differentiation between soils was apparent in the homoionic exchange reactions,
and the results can be summarized by saying that all soils preferred K to Na+ ,
and Rb and K + , in accordance with the expected order of selectivity (see
Section IV,B, 1). Adsorbed-ion activity coefficients showed no heterogeneity for
these cation pairs, preference for one ion over another being equally distributed
over all the exchange sites.
For Ca2+ + K + exchange, the characteristics were very different. Some
isotherms showed hysteresis, and that of a Harwell series soil exhibited selectivity reversal. Free energy changes showed that K+ was preferred to Ca2+ on
KEITH W.T. GOULDING
all the soils, and a comparison of enthalpy and entropy changes demonstrated
that this was always because of stronger binding of K+ (negative AH"),offset by
an increase in order (negative AS"). The soils differed greatly in their AGO, W ,
and ASO values because of differences in their clay and silt mineralogies. Graphs
of adsorbed-potassium activity coefficients (fK)versus K+ saturation exhibited
maxima, minima, and inflections (Fig. 2A). Later (Talibudeen, 1971, 1972)
these characteristics were qualitatively related to the clay mineralogy of the soils,
the assumption being that each maximum or inflection reflected a changeover of
Ca2 form to K form by one group of K -selective sites after another. It was
thought that such graphs might improve the description of soil mineralogies.
Excess functions (Section I1,F) were also used for this purpose, but being calculated from fK and fca values offered no additional information.
In relation to practical agriculture, Talibudeen (1971) thought that the change
in excess free energy with K + saturation expressed the reciprocal of the K +
buffering capacity of a soil (seealso Section IV,F,l). Soils in which this function
changed least as K + saturation approached zero were expected to release most
K+ . This was not tested experimentally, but changes infK (from which A P is
derived) as K+ saturation approached zero agreed qualitatively with K uptake
by ryegrass in pots from the soils. This and later work (Talibudeen and Weir,
1972) also explained the unusual K+-Ca2+ exchange characteristics of the
Harwell series soil mentioned earlier as the result of the presence of a zeolite,
clinoptilolite, mainly in the coarse clay and fine silt (0.3-5 pm) fraction of the
soil. Calorimetric measurements of enthalpies of K -Ca2 exchange have
shown that the interpretation of changes infK versus K + saturation curves and
excess functions in terms of mineralogical differences were correct (Goulding,
1980; Goulding and Talibudeen, 1980). The maxima in the former coincided
with the major steps in differential enthalpy curves from K+-selective to nonselective sites, as shown in Fig. 8, However, differential enthalpies were a much
better guide to heterogeneity and soil mineralogy than fK values because, being
directly measured by calorimetry, they were much more precise.
Similar enthalpy measurements on the separated particle size fractions of a soil
(Goulding and Talibudeen, 1979) showed the dominance of the fine (<0.2 pm)
and coarse (0.2-2 pm) clay fractions in determining exchange characteristics,
with the silt fraction making a small contribution. This work also showed that
because of irreversible changes in the clay surfaces brought about by the separation procedure the parts did not comprise the whole.
Further work on K+-Ca2+ exchange in temperate soils (Goulding and Talibudeen, 1984a,b) has shown more clearly how the exchange properties of soils
are determined predominantly by clay mineralogy and there is a complex interaction of this with pH, organic matter, and manurial history. A study of unfertilized
and K+-fertilized plots of eight soils with widely differing characteristics (pH